Thermal ringdown of a Kerr black hole: overtone excitation, Fermi-Dirac statistics and greybody factor

Abstract

We find a significant destructive interference among Kerr overtones in the early ringdown induced by an extreme mass-ratio merger of a massive black hole and a compact object, and that the ringdown spectrum apparently follows the Fermi-Dirac distribution. We numerically compute the spectral amplitude of gravitational waves induced by a particle plunging into a Kerr black hole and study the excitation of multiple quasi-normal (QN) modes. We find that the start time of ringdown is before the strain peak of the signal and corresponds to the time when the particle passes the photon sphere. When the black hole has the near-extremal rotation, the Kerr QN frequencies are close to the fermionic Matsubara frequencies with the Hawking temperature and the chemical potential of the superradiant frequency. We indeed find that the absolute square of the spectral amplitude apparently follows the Fermi-Dirac distribution with the chemical potential of around the real QN frequency of the fundamental mode. Fitting the Boltzmann distribution to the data in higher frequencies, the best-fit temperature is found out to be close to the Hawking temperature, especially for rapid rotations. In the near-extremal limit, the gravitational-wave spectrum exhibits a would-be Fermi degeneracy with the Fermi surface at the superradiant frequency ω = μ H. We show that the greybody factor, i.e., the absorption cross section of a black hole, leads to the Fermi-Dirac distribution. As the greybody factor is another no-hair quantity of black holes, this opens a new possibility that we could test general relativity by observationally searching for the Boltzmann distribution in ringdown, provided that near-extremal black holes exist in the observable region. Indeed, it has been predicted that near-extremal supermassive black holes would exist at the center of some galaxies from the X-ray reflection spectroscopy. We could measure the mass and angular momentum of ringing black holes and could probe the Kerr/CFT correspondence by measuring the greybody factor imprinted on the ringdown spectrum.

Quasinormal modes and grey-body factors of regular black holes with a scalar hair from the Effective Field Theory

“…In this work, we will take a further step and investigate not only the fundamental mode but also several first overtones of the EFT of gravitational perturbations of the Hayward spacetime. Although it is commonly believed that the principal contribution to the signal is due to the fundamental mode, recent research [17] (and subsequently examined in [18][19][20]) has demonstrated that in order to simulate the ringdown phase accurately, which is obtained within the precise numerical relativity simulations at the start of the quasinormal ringing and not just at the final stage, the first few overtones must be considered. This discovery also suggested that the actual QN ringing begins earlier than expected.…”